Well, yes, stress may cause droopy eyelids. And generally speaking, stress can just tighten your eye skin, and then in a long term, it will just affect your eyelid, leading to droopy eyes. Droopy eyelids can make you look tired and older than you really are. At this moment, you can use some tea bags to treat it. And it has a great effect on eyelids. After you have drunk your daily tea, you can just put the teabags in the refrigerator until these become cool, and then just apply them on your eyes. Also, you can try some sunscreen too. Anyway, just have some try.
It is very possible for you to get droopy eyelids because of stress. When you get the great stress from the busy work, your eye muscles will be in the intense state often which will easily cause the droopy eyelids. However, the droopy eyelid will also be caused by the lack of good sleep. You should relax your mood, have the good rest, have the good diet and so on. You must protect the eyes part.
All right, from what I can see, you are worried about your droopy eyelid, Anyway, it is a very complicated problem which could be classified into different types. So, stress or something like fatigue, would make droopy eyelid much more serious and worse. So once you got droopy eyelid, you should take positive actions against it and try to relax yourself and keep in a good mood.